Additive commutators of operators belonging to two{sided ideals of B(H) are studied. J){commutators is characterized and found to equal IJ ; B(H)]. It is shown that three commutators are enough in I; B(H)], and that four are enough in I; J ]. Finally, some results about single commutators are proved, for example that every element of the Schatten class C p is a single (C p ; B(H)){commutator if...

In this note self-adjoint realizations of second order elliptic differential expressions with non-local Robin boundary conditions on a domain Ω ⊂ Rn with smooth compact boundary are studied. A Schatten–von Neumann type estimate for the singular values of the difference of the mth powers of the resolvents of two Robin realizations is obtained, and for m > n 2 − 1 it is shown that the resolvent p...

Let A be a Hilbert-space operator satisfying the growth condition ||(z —/4) || < expi&[dist(z, /)]~SS, z //.where / is a C Jordan curve, and K > 0, s £ (0, 1) are two constants. Let T = A + B for some fi e C , I < p < oc. It is shown that T is strongly decomposable if and only if cr(T') does not fill the "interior" of /. 1, H. Radjavi and the author [13] showed that if a Hilbert-space operator ...

0. Introduction. Let us begin by recalling brieey some salient facts from classical Hankel theory (cf. Ni]). Consider the Hardy class H 2 (T), where T is the unit circle in C , and let H 2 (T) ? be its orthogonal complement in the space L 2 (T). If is a holomorphic function, one deenes the Hankel operator H with symbol by the formula H f = P ? f (f 2 H 2 (T)) where P ? stands for orthogonal pro...

Sketching is a prominent algorithmic tool for processinglarge data. In this paper, we study the problem of sketchingmatrix norms. We consider two sketching models. The firstis bilinear sketching, in which there is a distribution overpairs of r×n matrices S and n× s matrices T such that forany fixed n×n matrix A, from S ·A ·T one can approximate‖A‖p up to an approxima...

Let f be a multiplier for the Drury-Arveson space H n of the unit ball, and let ζ1, ..., ζn denote the coordinate functions. We show that for each 1 ≤ i ≤ n, the commutator [M∗ f ,Mζi ] belongs to the Schatten class Cp, p > 2n. This leads to a localization result for multipliers.

Let ii be a bounded symmetric domain in C with normalized 2 volume measure dV . Let P be the orthogonal projection from L (il, dV) 2 2 onto the Bergman space La(Q) of holomorphic functions in L (ii, dV). Let P be the orthogonal projection from L (ii, dV) onto the closed subspace of antiholomorphic functions in L (ii, dV). The "little" Hankel operator h, with symbol / is the operator from La(Ci)...

We consider convex sets whose modulus of convexity is uniformly quadratic. First, we observe several interesting relations between different positions of such “2-convex” bodies; in particular, the isotropic position is a finite volume-ratio position for these bodies. Second, we prove that high dimensional 2-convex bodies posses one-dimensional marginals that are approximately Gaussian. Third, w...